SRG/eROSITA-SDSS view on the relation between X-ray and UV emission for quasars

TL;DR

The paper addresses whether quasars can serve as standardizable candles by quantifying the nonlinear L_{2keV}-L_{2500} relation. It develops a rigorous joint model in log-luminosity space that incorporates a primary linear dependence, intrinsic scatter in both L_{2keV} and L_{2500}, a luminosity-function-driven selection effect, and quasar variability across multiple timescales, analyzed with MCMC. Applying the method to 2414 SRG/eROSITA--SDSS quasars in 0.5<z<2.5, the authors measure a slope $\gamma=0.69\pm0.02$ and a normalization $l_{\rm X}=26.45\pm0.02$ at $l_{\rm UV}=30.5$, finding a dominant intrinsic X-ray scatter $\sigma^2_{ m intX}=0.066\pm0.005$ and a much smaller UV scatter $\sigma^2_{ m intUV}=0.001^{+0.003}_{-0.001}$. The analysis demonstrates that selection biases and variability significantly affect the inferred relation, with intrinsic X-ray dispersion likely tied to SMBH mass, accretion rate, and orientation. The results refine constraints on using quasars as distance indicators and illuminate SMBH accretion physics, while supporting the consistency of the X-ray LF with prior work and highlighting avenues for future synchronized multiwavelength campaigns.

Abstract

Motivated by the idea of using quasars as standardizable candles for cosmology, we examine the relation between X-ray (at 2 keV, $L_{\rm 2keV}$) and ultraviolet (at 2500 Angstrom, $L_{\rm 2500}$) monochromatic luminosities of quasars using a sample of 2414 X-ray sources from the SRG/eROSITA all-sky survey cross-matched with the Sloan Digital Sky Survey data release 16 quasar catalogue (SDSS DR16Q), at redshifts between 0.5 and 2.5. These objects are bright both in X-rays and in the optical, so that the sample is characterized by nearly 100% statistical completeness. We have developed a new method for determining the $L_{\rm 2keV}-L_{\rm 2500}$ relation, which consistently takes into account (i) X-ray and UV flux limited object selection, (ii) X-ray and UV variability of quasars, and (iii) the decreasing space density of quasars with increasing luminosity. Assuming a linear relation between $l_{\rm X}\equiv\log(L_{\rm 2keV}/[{\rm erg\,s^{-1}\,Hz^{-1}}])$ and $l_{\rm UV}\equiv\log(L_{\rm 2500}/[{\rm erg\,s^{-1}\,Hz^{-1}}])$, we find the slope, $γ=0.69\pm0.02$ (hereafter all uncertainties are quoted at the 68% confidence level), and normalization, $l_{\rm X}=26.45\pm0.02$ at $l_{\rm UV}=30.5$, of the $L_{\rm 2keV}$ ($L_{\rm 2500}$) dependence. These values are not substantially different from the results of previous studies. A key novel aspect of our work is allowance for intrinsic scatter (which adds to the dispersion induced by quasar variability and flux measurement uncertainties) of the $L_{\rm 2keV}-L_{\rm 2500}$ relation in both variables, i.e. in X-ray and UV luminosity. The intrinsic X-ray scatter ($σ^2_{\rm intX}=0.066\pm0.005$) strongly dominates over the UV one ($σ^2_{\rm intUV}=0.001^{+0.003}_{-0.001}$). Further studies should seek to explain this behaviour in terms of accretion onto supermassive black holes and orientation of quasars with respect to the observer.

Figures (18)

• Figure 1: Solid lines show $\log{K_{\rm X}(z,\Gamma)/K_{\rm X}(z,2)}$ as a function of $z$ for different X-ray spectral indexes $\Gamma$, as indicated in the legend. The black dashed line marks the mean values of the $\log{\left[K_{\rm X}(z,\Gamma)/K_{\rm X}(z,2)\right]}$ distribution as a function of $z$ and assuming that $\Gamma$ follows a normal distribution with $\mu=2$ and $\sigma=0.3$. The black dashed semitransparent lines mark the mean plus one standard deviation and the mean minus one standard deviation as a function of $z$. Hereafter, $\log$ means $\log_{10}$.
• Figure 2: Top panel: Scatter-plot of $k$-correction vs redshift for quasars from our sample before the additional UV luminosity selection. The red dashed line bounds the region containing 99% of objects in each redshift bin. Bottom panel: Corresponding scatter-plot of 2500Å luminosity vs redshift. The black line depicts the luminosity limit $L_{\rm 2500min}$ as a function of $z$.
• Figure 3: Scatter-plot of the logarithms of X-ray luminosities vs. their uncertainties for the SRG/eROSITA--SDSS quasar sample. The histograms shown on the sides reflect projections of the two-dimensional distribution on the corresponding axes (note the logarithmic scale for the number of objects).
• Figure 4: Scatter-plot of the logarithms of UV (2500 Å) luminosities vs. their uncertainties for the SRG/eROSITA--SDSS quasar sample. The histograms shown on the sides reflect projections of the two-dimensional distribution on the corresponding axes (note the logarithmic scale for the number of objects).
• Figure 5: Distribution of SDSS $g$-band photometric magnitudes for the SRG/eROSITA--SDSS quasar sample. The full sample is shown in green. The other histograms show subsamples according to SDSS spectroscopy: blue, quasars observed in SDSS I/II only; orange, those observed in SDSS III/IV only; red, those observed both in SDSS I/II and SDSS III/IV.